Greig played one-day cricket as an all rounder for Sussex County Cricket Club in 1979 before making his first-class debut for the team in 1980. His career with Sussex lasted until 1985. His most successful season for Sussex was in 1981, when he scored 911 runs (average 30.36), and took 76 wickets at 19.32. In 1982, the English selectors chose him as a replacement for the injured Derek Pringle to face Pakistan in two test matches.[3]

Sussex released Greig, and others, in 1985 as part of cost-cutting measures, and Greig emigrated to Australia. However, he joined Surrey County Cricket Club, and captained the team between 1987 and 1991.[3]